Problem: $A$ $B$ $C$ If: $ AC = 88$, $ AB = 4x + 6$, and $ BC = 6x + 2$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {4x + 6} + {6x + 2} = {88}$ Combine like terms: $ 10x + 8 = {88}$ Subtract $8$ from both sides: $ 10x = 80$ Divide both sides by $10$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $BC$ $ BC = 6({8}) + 2$ Simplify: $ {BC = 48 + 2}$ Simplify to find ${BC}$ : $ {BC = 50}$